On stability of the P n mod / P n element for incompressible flow problems

Petr Knobloch

Applications of Mathematics (2006)

  • Volume: 51, Issue: 5, page 473-493
  • ISSN: 0862-7940

Abstract

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It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of n th order accuracy in the energy norm called P n elements. For n ≤ 3 we show that the stability condition holds if the velocity space is constructed using the P n elements and the pressure space consists of continuous piecewise polynomial functions of degree n .

How to cite

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Knobloch, Petr. "On stability of the $P^{\rm mod}_ n/P_ n$ element for incompressible flow problems." Applications of Mathematics 51.5 (2006): 473-493. <http://eudml.org/doc/33263>.

@article{Knobloch2006,
abstract = {It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of $n$th order accuracy in the energy norm called $P_n^\{\}$ elements. For $n\le 3$ we show that the stability condition holds if the velocity space is constructed using the $P_n^\{\}$ elements and the pressure space consists of continuous piecewise polynomial functions of degree $n$.},
author = {Knobloch, Petr},
journal = {Applications of Mathematics},
keywords = {nonconforming finite element method; inf-sup condition; incompressible flow problem; nonconforming finite element method; inf-sup condition; incompressible flow problem; incompressible flow},
language = {eng},
number = {5},
pages = {473-493},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On stability of the $P^\{\rm mod\}_ n/P_ n$ element for incompressible flow problems},
url = {http://eudml.org/doc/33263},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Knobloch, Petr
TI - On stability of the $P^{\rm mod}_ n/P_ n$ element for incompressible flow problems
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 5
SP - 473
EP - 493
AB - It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of $n$th order accuracy in the energy norm called $P_n^{}$ elements. For $n\le 3$ we show that the stability condition holds if the velocity space is constructed using the $P_n^{}$ elements and the pressure space consists of continuous piecewise polynomial functions of degree $n$.
LA - eng
KW - nonconforming finite element method; inf-sup condition; incompressible flow problem; nonconforming finite element method; inf-sup condition; incompressible flow problem; incompressible flow
UR - http://eudml.org/doc/33263
ER -

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